I’ve just finished reading Max Tegmark’s latest book, ‘Our Mathematical Universe‘, about his views on multiverses and the ultimate nature of reality. This is the first in a series of posts that I plan to do on it. Tegmark postulates four levels of multiverse. This post is about the first, and simplest version, the Level I Multiverse.

No one knows for sure how large the universe is, but the size of the observable universe is actually pretty well known. The universe as we know it started expanding from a hot dense state about 14 billion years ago. Given the fast but finite speed of light, the further away we look, the further back in time we’re looking.

The furthest and oldest thing we can now see is the cosmic microwave background (CMB), which has been traveling for almost the entire history of the known universe, 14 billion years. However, due to the expansion of space, the CMB we are now seeing originated 46 billions light years away, making that the radius of the observable universe.

Cosmologists often consider the word “universe” to be synonymous with the observable universe. The reason for this is it’s all we can observe, and given that the speed of light is the fastest speed that any interaction or effect can travel, the edge of the observable universe is the limit of our causal influence, or of things that could influence us. In other words, we are currently causally disconnected from the regions beyond this point, beyond or cosmological horizon.

Of course, there’s no real reason to think the universe ends at the limits of our observation. Indeed, attempts to measure the curvature of space seem to indicate that the whole universe is at least hundreds of times the size of the observable universe.

Considering the observable universe to be our universe, Tegmark refers to the regions beyond as other universes. Semantically, this seems like a questionable move. These regions seem like more of just the same universe. Initially I suspected this might be an attempt to redefine the multiverse into something non-controversial so the controversial versions wouldn’t be as much of a leap.

However, if the universe is infinite, it leads to strange conclusions, and with enough distance, the phrase other universes starts to make sense. Within each local observable universe, there are a finite number of ways that the atoms can be arranged. (Note: a very large number of combinations, but a finite number.) This means that in an infinite universe, every possible configuration of matter will eventually be realized. Furthermore, if you could look far enough in this infinite space, eventually every configuration will repeat itself, infinitely.

In other words, in an infinite universe, somewhere there would be another observable universe, also with a 46 billion light year radius, that is identical to ours. If so, it would contain a duplicate version of you reading a duplicate of this blog entry. Actually, throughout infinite space, there would be infinite copies of you reading infinite copies of this blog entry. And there would be an infinite number of you in every possible variation of you leading every possible variation of your life.

These duplicate universes would exist within the same space that we inhabit, have the same laws of physics, and the same or varying histories. But even the closest would be unimaginably far way. Tegmark states that current calculations show that it would be 101029 meters from here, which of course is an indescribable distance.

Do these duplicate regions, these parallel universes, exist? If space is infinite, or at least 101029 meters in extent, it seems hard to argue that they don’t. If space is that large. But we don’t know yet whether or not it is. It might be, or it might not be.

Current measurements show space to be flat, but as I said above, the margin of error on these measurements leaves room for space to still eventually loop back onto itself, to make it that if you could travel in a certain direction long enough, you’d end up back at your starting point, similar to what happens on Earth, but in three dimensions.

But if space is flat and infinite, and these duplicate regions do exist, it’s hard to imagine how their existence could ever have an effect on us (unless maybe if someone invented an intergalactic warp drive). This also seems to make the idea unfalsifiable. Still, the concept, while speculative, is a fascinating one.

This is the simplest of the multiverses that Tegmark discusses in his book. In the next post in this series, I’ll discuss his Level II Multiverse.

28 Responses to Tegmark’s Level I Multiverse: infinite space

My main problem with calling the level one multiverse a collection of different universes is that these universes overlap enormously. I think a true multiverse ought to have distinct non-overlapping universes so that two observers can agree that they are in the same universe and no other. Even two earthbound humans can’t do that do that as your level I universe is very slightly different from mine, being centred on you.

I don’t think the level I multiverse is unfalsifiable. Tegmark makes the point that when a theory makes predictions that are not themselves observable, they are nevertheless falsifiable by finding that the theory doesn’t work in other respects. But the level I multiverse is clearly falsifiable. We could for instance find that space is too curved to extend much beyond the cosmic horizon, or see that space repeats by observing similarities and mirror images in what we see looking northwards and looking southwards. So far, the level I multiverse has survived such attempts to falsify it, which is hardly something to hold against it.

It’s also not a concept completely without practical implications. If there really are an infinite number of duplicates of you, that raises important questions about personal identity. If there is absolutely no difference between you and your clone, then does it even make sense to regard the two as distinct entities? If one of you were to suddenly die, and the other to live, would that not constitute a continuation of your identity? Might this not imply immortality?

Thanks. I agree on the naming issue for space just outside of our observable universe, but have some sympathy with calling the space 10^10^29 meters away another universe. I can see where you’re coming from on falsifiability.

I’m not sure about “practical” implications, but I do plan to discuss subjective immortality. I was holding off on that until after the Level III description.

On practical implications, I just mean that subjective immortality might have implications for decision-making where risk of death comes into it and in the whole outlook towards death in general. It makes suicide futile, for instance.

Hmmm, not sure if I buy that. If I’m in pain, and choose to end it, even if some versions of me might choose to endure, I can’t see how the local dead instance of me would feel their suffering. Likewise, if I’m in danger of death, it seems cold comfort that some putative versions of me somewhere will live on. In my local universe, I’d still be gone. Unless we start imagining things like joined consciousness or something.

That’s where it gets interesting. If there really is no difference between you, then I’m inclined to think there is no distinction.

Your argument assumes that it makes sense to identify yourself with a particular bunch of atoms, but if all the atoms in your body were swapped with identical ones one by one you would never know the difference (and essentially this is actually happening all the time due to natural processes).

So you’re not just a bunch of atoms. You are something about the way the atoms are arranged. But if the other you is arranged in the same way, then it is also you.

You could characterise this as joined consciousness but I wouldn’t see it as spooky or mysterious.

I’m not claiming this is the correct way to think of personal identity. I don’t think there is any satisfactory way really. Personal identity is a human intuitive concept that doesn’t really hold up to analysis, but this is my preferred way to think about it.

Obviously given the name of this site, I’m totally on board that we’re patterns, not the atoms that happen to make us up at the moment. And I think I’d take comfort if there was a copy of me within sight, that I knew existed, when my current instance lay dying. But I don’t really have enough faith in unseen copies, at least currently, for them to be of much comfort.

Personal identity is definitely a human intuition. One we evolved due to its survival advantage. Indeed, the very desire to have our pattern continue, to survive, is simply evolved programming. There’s no reason to want to survive, other than the urge. Still, knowing that doesn’t make the urge go away.

“Semantically, this seems like a questionable move. These regions seem like more of just the same universe. Initially I suspected this might be an attempt to redefine the multiverse into something non-controversial so the controversial versions wouldn’t be as much of a leap.”

Funny, i had the exact same thought when i first heard it presented like this.

“Throughout infinite space, there would be infinite copies of you reading infinite copies of this blog entry. And there would be an infinite number of you in every possible variation of you leading every possible variation of your life.”

Dang, I hope space is as vast as they say, that way I’d have the comfort of knowing that in some universe I wouldn’t actually be living in Virginia.

Thanks for sharing your thoughts on this, it is a topic of which I know little and am excited to read your writing on the matter. Looking forward level II.

It doesn’t seem like we could ever remove doubt that the universe is merely insanely big instead of infinite. Of course, any indication that space eventually loops back on itself would falsify infinity.

I certainly did not imply that it was a crazy idea, merely that infinities should be treated with the utmost respect and caution. And as you say, a well-validated theory that predicts and explains an infinite universe would be compelling proof.

My view is that an approximately flat universe could be either finite or infinite, and there’s no compelling reason to assign either a much greater probability. I do somewhat lean towards infinite though, if only because it’s neater.

One question that Physics must one day answer is, where did it all come from? I’m talking about mass-energy conservation. The most likely explanation seems to me that everything adds up to zero somehow. But if not, then creating a finite amount of stuff out of nothing is potentially explicable, but creating an infinite amount seems implausible.

I don’t follow why an infinite amount of stuff is implausible. Infinities can cancel out just as well as finite amounts.

In any case, my understanding is that gravitational energy is negative, so we already have a model whereby everything cancels out – the mass and energy itself is positive, the way it warps space is negative. This would be true whether the universe is finite or infinite, because the average energy density is zero even at reasonably local scales.

So if the energy density is zero throughout, infinite zeros add up to infinity.

I don’t pretend to understand this, but it has something to do with inflation.

Neither is really plausible, but a finite amount if finitely implausible and an infinite amount infinitely implausible 🙂 I could be wrong. If energy is like numbers, then creating all of them is perhaps no harder than creating one.

Cool stuff. While I think the Universe is big (and mean really f*****’ big, if inflationary theory is correct) I doubt is infinite. That data shows it may simply mean its curvature is too small to be detectable for now (and the “circles in the sky” may not exist because light has not had time to circumnavegate the Universe). Same for some papers, that analyzing data from the Planck mission have ruled out certain geometries for the ‘verse.

Good points. I remember reading somewhere that the “actual” universe has to be at least 250 times the size of the observable one, assuming the curvature of space exists within the margin of error of our measurements.

I’m personally agnostic on the infinity part. You could be right though. Looking at the history of cosmology, scientists have a tendency to project infinity beyond current observations, because it’s mathematically simple. But the universe seems to have no obligation to adhere to our notions of simplicity.